C. Jakowatz, D. Wahl, P. Eichel, D. Ghiglia, and P. Thompson have provided a valuable service to the signal processing community. Their algorithm description for phase gradient autofocus (PGA; section 4.5, pages 251 -269) is clear, consistent and illuminating. PGA is a robust, “non-parametric estimator that exploits redundancy of aperture phase error across multiple range lines”.

” The PGA algorithm consists of four critical steps: center (circular) shifting, windowing, phase estimation, and iterative correction.” Jakowitz et al. report that all four steps must be executed to achieve good performance. They define a phase estimator that achieves maximum likelihood optimality (i.e., the phase error approaches its Cramer-Rao lower bound). Once the bulk delay due to range walk is corrected (parametrically), PGA processing converges rapidly. The algorithm can be used in any domain (radar, acoustics, laser, etc.) where synthetic aperture processing (spotlight or stripmap) is performed.